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That's it. A total of three tools provide everything you need to figure out what's going on during a raid. It won't give you everything, but it's enough to figure out what went wrong and who screwed the pooch.

Recount
Beloved epeen meter for both DPS and healers the world over. Recount provides a massive amount of information per fight. I primarily use it to figure out why people died. However, I've also used it to spot check healer output, who healers are actually healing, and what spell mix they use. For DPS, I just glance at it and yell at whoever is low. While it doesn't really allow you to see which "special raider" broke the shields on Omnotron, it's "good enough" for debugging issues while you raid.

Grid:
The classic raider's unit frames... or whatever current equivalent you like to use (healbot/VuhDo/default Blizzard frames). Mainly useful to see two key pieces of information:

1) Who's in healing range. If they're not in healing range, use that nifty voice communication program called Mumble to ask if someone else has them in range. I know, communication... a novel concept.

2) Who's taking a dirt nap. Depending on the encounter, sometimes you can see that someone is dead, but who the fuck cares. Their useful period had already passed. Let them stay dead and save the rez for someone you need in order to complete the fight.

Grid Raid Debuff:
One of the best addons for Grid. Massively useful when healing and/or seeing who has what debuff. If you don't have it, get it. I believe the functionality is included in the various other unit frames as a part of the package. Grid raid debuffs let you call out tank swaps and other raid debuffs as needed.